Score-Based Generative Model With Conditional Null-Space Learning for Limited-Angle Tomographic Reconstruction in Medical Imaging

Limited-angle computed tomography (LA-CT) reconstruction represents a typically ill-posed inverse problem, frequently resulting in reconstructions with noticeable edge divergence and missing features. Score-based generative models (SGMs) based reconstruction methods have shown strong ability to reconstruct high-fidelity images for LA-CT. Data consistency is crucial for generating reliable and high-quality results in SGMs-based reconstruction methods. However, existing deep reconstruction methods have not fully explored data consistency, resulting in suboptimal performance. Based on this, we proposed a Conditional Score-based Null-space (CSN) generative model for LA-CT reconstruction. First, CSN integrates prior physical information of limited-angle scanning as conditional constraint, which can enable SGMs to obtain more accurate generation. Second, in order to balance the consistency and realness of the reconstruction results, the range-null space decomposition strategy is introduced in the sampling process. This strategy ensures that the estimation of the information occurs only in the null-space. Finally, we employ the sparse least square (LSQR) instead of commonly used consistency terms such as simultaneous iterative reconstruction technique (SIRT), thereby achieving superior reconstruction results. In addition, a mathematical convergence analysis of our CSN method is provided. Experimental evaluations on both numerical simulations and real-world datasets demonstrate that the proposed method offers notable advantages in reconstruction quality.